The Effect of an Ocean-Land Mixed Propagation Path on the Lightning Electromagnetic Fields and Their Induced Voltages on Overhead Lines

8/9/2019 The Effect of an Ocean-Land Mixed Propagation Path on the Lightning Electromagnetic Fields and Their Induced Volt…

http://slidepdf.com/reader/full/the-effect-of-an-ocean-land-mixed-propagation-path-on-the-lightning-electromagnetic 1/8

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 30, NO. 1, FEBRUARY 2015 229

The Effect of an Ocean-Land Mixed Propagation Pathon the Lightning Electromagnetic Fields and Their

Induced Voltages on Overhead LinesKeyhan Sheshyekani , Senior Member, IEEE , and Javad Paknahad , Student Member, IEEE

Abstract— We use a full-wave approach based on the nite-ele-ment method solution to Maxwell's equations for the evaluation of the effect of an ocean-land mixed propagation path on the above-ground lightning electromagnetic elds and their induced voltageson overhead lines. Two cases of normal and oblique strikes arestudied. For normal strike, it is shown that neither the vertical elec-tric eld nor the azimuthal magnetic eld is affected by the con-sidered mixed propagation path. For an oblique strike, however,the azimuthal magnetic eld is slightly affected when the observa-

tion point is close to the ocean-land interface (i.e., 5 m o r so), whilethe vertical electric eld remains unchanged. For both normal andoblique strikes, at moderate and far distances from the channelbase and when the observation point is located in the vic inity of theocean-land interface, the radial electric eld is markedly affectedby this interface. For the calculation of lightning-induced voltages,two cases, namely, the ocean-side and the river-crossing transmis-sion lines are studied. For the ocean-side transmission line, as theoverhead line gets closer to the ocean, the induced voltages on theline midpoint decrease while increasing beha vior is observed in thevoltages induced on the line terminations. For the river-crossingtransmission line, the lightning-induced voltages along the line ex-perience a signicant change in terms of their peak values andwaveshapes. In some cases, the enhancement in induced voltagescan be as high as a factor of 2 with respect to that obtained byassuming a homogeneous propagation pa th characterized by theelectrical properties of the land.

Index Terms— Electromagnetic elds, nite-element method(FEM), lightning-induced voltages, ocean-land mixed propagationpath.

I. I NTRODUCTION

T HERE HAS been a growing interest over the last fewdecades, for accurate modeling of lightning interaction

with nearby overhead transmission lines. The relevance ismainly due to the fact that lightning electromagnetic eldscan induce severe voltage stress on power system equipment.These overv oltages, in particular, for distribution electricalsystems, can result in insulation breakdown, fault initiation, andconsequential line outages as well as deteriorating the power

Manuscript received January 07, 2014; revised May 24, 2014; accepted July10, 2014. Date of publication July 28, 2014; date of current version January 21,2015. Paper no. TPWRD-00012-2004

The authors are with the Electrical and Computer Engineering Department,Shahid Beheshti University, Velenjak, Tehran 1983963113, Iran (e-mail:[email protected]).

Color versions of one or more of the gures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identier 10.1109/TPWRD.2014.2339096

quality of the utility networks. The overall modeling proceduregenerally involves: 1) lightning return stroke modeling [1];lightning electromagnetic pulse (LEMP) computation [2],[3]; and LEMP-to-overhead line coupling calculation [4]–[6].The rst developed models for calculating lightning-radiatedelectromagnetic elds and their induced voltages on overheadlines consider the ground as a homogeneous ideal or lossymedium (e.g., [1]–[8]). However, this assumption is not alwaysvalid in the sense that the ground might consist of differenthorizontal or vertical layers whose electrical par ameters arefrequency dependent [10] and [11]. Hence, a precise evaluationof lightning-induced voltages on overhead lines is not possibleunless the exact model of the ground is taken int o account. Withthis regard, two critical issues at play are the multilayer soilstructure and the frequency dependence of soil electrical pa-rameters. Recently, the effect of freq uency dependence of soilelectrical parameters on the lightning electromagnetic elds[9], [12] and their interaction with single and multiconductor overhead lines [12] and [13] has been elaborately discussed.Furthermore, there has also been an increasing tendency for the evaluation of lightning electromagnetic elds above andinside a horizontal or verti cal two-layer stratied ground. Sofar, these attempts have succeeded in predicting the lightningelectromagnetic elds above and inside horizontal two-layer grounds mostly at close d istances from the lightning channel base. The early works that studied the wave propagation alonga vertically stratied ground (also called the mixed propagation path) are mainly tho se presented by Millington [14], Suda[15], and Bremmer [16]. The concept of attenuation function presented by Wait [17] and [18] has been used by Shoory et al. [19] for the e valuation of lightning electromagnetic eldsover a mixed propagation path showing that the Wait's formulais only able to reproduce the lightning electromagnetic eldsfor distant observation points. Recently, Zhang et al. [20]have managed to modify the Cooray–Rubinstein formula ina way to use it for the evaluation of lighting electromagneticelds abo ve a smooth ocean-land mixed path. The accuracyof the method is, however, limited to conductivities rangingfrom 0.01 to 0.001 S/m when the elds propagate from theocean surface to the land section [21]. More recently, a nitedifference approach has been used to determine the effectof a horizontally stratied ground on the lightning-inducedvoltages on overhead lines [22]. Furthermore, the effect of horizontally and vertically stratied ground on the underground

0885-8977 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.



230 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 30, NO. 1, FEBRUARY 2015

lightning electromagnetic elds and their induced currents onthe buried cables have been recently evaluated in [23] and [24].Therefore, more investigations are required to study the effectof soil vertically stratication on the above-ground lightningelectromagnetic elds and their associated induced voltages onthe nearby overhead lines.

Within this context, this paper focuses on the analysis of theeffect of an ocean-land mixed propagation path on the light-ning-radiated electromagnetic elds at different distances fromthe channel base as well as on their associated induced volt-ages on overhead lines. The cases of normal and oblique in-cidences are discussed. The lightning-induced volt ages on anoverhead transmission linecrossing over a river are alsostudied.To this aim, we use a full-wave approach which is based on thenite-element method (FEM) solution of Ma xwell's equations.The developed model allows the evaluation of the above-groundlightning electromagnetic elds and the induced voltages on theoverhead lines located above a vertic ally stratied ground.

This paper is organized as follows. In Section II, the -nite-element modeling of the problem is briey discussed.In Section III, the effect of a n ocean-land mixed propagation path on the above-ground lightning electromagnetic eldis evaluated. Section IV discusses the same effect on thelightning-induced volt age on an ocean-side overhead line. InSection V, the lightning-induced voltages on a river-crossingoverhead line are discussed. Finally, some general conclusionsare presented in Section VI.

II. FULL -W AVE FINITE -ELEMENT MODELING

The electromagnetic wave (EMW) solver of the RF-Moduleof the COMSOL multiphysics [25] is utilized for the calculationof lightning electromagnetic elds and their induced voltages onoverhead lines (e.g., [12] and [13]). This enables us to calculatethe lightning electromagnetic elds in 2-D and 3-D spaces in thetime domain. To this end, the weak-form representation of thetime-domain wave equation of the magnetic vector potential issolved by the nite-element method [26].

The geometry of the problem is shown in Fig. 1. In thisconguration, the mixed propagation path involves the landand the ocean which are, respectively, characterized by con-ductivity and relative permittivity of and .In COMSOL, Natural Neumann conditions are used in thesoil-air and in the soil-ocean interfaces, while the naturalDirichlet conditions are imposed on the solution domain asthe external boundary condition [12]. In our modeling, theradius of the overhead line wire and the lightning channel arevery small compared to the mesh dimensions. Due to this factand to avoid a large and inefcient matrix system in the FEMformulation, the conductor wire is reasonably modeled as asequence of mesh edges (as in [12] and [13]). To apply thenite-element approach to open region problems, such as for lightning radiated electromagnetic elds study, an articial boundary is introduced in order to dene the region of analysisand to limit the number of unknowns to a manageable size. For this purpose, the scattering boundary condition available in theRF module is used in order to prevent the waves from beingreected by the boundaries [25].

Fig. 1. Geometry for the calculation of lightning electromagnetic elds abovea vertically stratied two-layer ground (ocean-land mixed propagationpath). (a)Side view. (b) Top view.

TABLE IHEIDLER 'S PARAMETERS FOR SUBSEQUENT STROKE A DOPTED FROM [27]

In this study, the modied transmission line with an exponen-tial decay model (MTLE) is adopted for modeling the lightningreturn stroke channel with a current height decay of 2000m, assuming a return stroke speed of m/s, ac-cording to which the current distribution along the channel isspecied as

(1)

where is the channel current at height denotes the re-turn stroke speed, and is the current height decay constant. Asfor the lightning channel-base current, we use Heidler's functionwhose parameters are listed in Table I [27]. Note that the sumof two Heidler's functions is used to represent the subsequentreturn stroke current [28].

III. E FFECT OF THE OCEAN -LAND MIXED PROPAGATION PATH

ON THE A BOVE -GROUND LIGHTNING EM F IELDS

With reference to Fig. 1, we aim at evaluating the lightning-radiated electromagnetic elds above the ground at 10






Fig.4. Horizontal component oftheelectric eld at10 m above anocean-land mixed propagation path: (a) 50 m, (b) 300 m, (c) 1000m. Observation point (normal strike). Return stroke current typical of sub-sequent strokes.

Fig. 5. Different components of the lightning electromagnetic elds at 10 mabove an ocean-land mixed propagation path for 300 m and 316 m.(a) , (b) , (c) ,. Observation point (oblique strike). Return strokecurrent typical of subsequent strokes.

of the ocean-land interface (i.e., 5 m or so). Moreover, contraryto thecase of normal strike, theazimuthal magnetic eld at closevicinity of the ocean is slightly affected by the considered mixed propagation path showing a modest increase with respect to thecase of the homogeneous soil with the same properties of theland.

Fig.6. Geometry forthe calculation of lightning-induced voltages on an ocean-side overhead line. The case of land strike.

Fig.7. Geometry forthe calculation of lightning-induced voltages on an ocean-side overhead line. (a) Top view. (b) Side view. The case of land strike.

It is worth mentioning that the validity of the proposed approach for calculating the lightning electromagnetic elds andtheir induced voltages on overhead lines has been comprehen-sively discussed in recent works by comparing the results withthe NEC and the LIOV code (see [13]).

IV. L IGHTNING -I NDUCED V OLTAGES ON OCEAN -S IDE

OVERHEAD L INES

A. Land Strike

The geometry of the problem is shown in Fig. 6 for whichthe top view and the side view are also shown in Fig. 7. Werst consider the case of a lightning strike to the land surface,referred to as a “land strike.” The single conductor overheadline is located entirely above the land which is referred to as“ocean-side overhead line.” The line has a length of 1000m, matched at both sides and its height above the ground is

10 m. The lightning channel is 50 m away from the linecenter and equidistant to the line ends. The land and the oceanare characterizedby the sameproperties presented in SectionIII.

Simulations are performed for different distances between theoverhead line and the ocean. Note that in doing so, we keep the



SHESHYEKANI AND PAKNAHAD: EFFECT OF AN OCEAN-LAND MIXED PROPAGATION PATH 233

Fig. 8. Induced voltages on the midpoint of the ocean-side matched over-head line shown in Fig. 7 due to a typical subsequent return stroke. The case of land strike.

Fig. 9. Total vertical electric eld at , 5 m right beneath the line center pointas shown in Fig. 7. Return stroke current typical of subsequent strokes.

distance between the overhead line and the lightning channelconstant for all situations. Following the procedure described in[12], the induced voltage is determined by integrating the totalvertical component of the electric eld along a vertical path be-tween the line conductor surface and the ground surface. Light-ning-induced voltages on the midpoint of the overhead line ,due to a typical subsequent return stroke (see Table I) are shownin Fig. 8 for different distances between the overhead line andthe ocean. Results associated with the case of homogeneous soilcharacterized by the electrical properties of the land are alsoshown in Fig. 8. As can be seen from Fig. 8, when the lightningchannel strikes on the land surface, as the overhead line getscloser to the ocean, the induced voltages on the line midpointshow decreasing behavior. In fact, when increasing the distance between the overhead line and the ocean, this induced voltage becomes closer to the case of homogeneous soil characterized by the land electrical properties. As discussed in the previoussection, the effect of the ocean-land mixed propagation path onthe vertical component of the electric eld in free space and inthe absence of the overhead line is negligible. As known, the in-duced voltage is obtained by integrating the total vertical elec-tric eld along a vertical path between the conductor surface andthe ground surface. Hence, in a similar way, any change in theinduced voltage should be justied by the associated change inthe total vertical electric eld.

It should be pointed out that by the total vertical electric eld,we mean the sum of the exciting electric eld generated by thelightning channel in the absence of the overhead line and thescattered electric eld that is the eld generated by the inducedcurrents and charges along the line. To further clarify this issue,Fig. 9 shows the total vertical electric eld calculated atwhich is 5 m beneath the center point of the line conductor [seeFig. 7(b)]. It is seen from this gure that, unlike the exciting ver-tical electric eld, the total vertical component of the electriceld is inuenced by the ocean-land mixed propagation path.

Fig. 10. Induced voltages on the termination of the ocean-side matchedoverhead line shown in Fig. 7 due to a typical subsequent return stroke. Thecase of ocean strike.

Fig.11. Totalverticalelectriceldat , 5 m rightbeneath theline terminationas shown in Fig. 7. Return stroke current typical of subsequent strokes.

Hence, the induced voltage, which is an integration of the ver-tical component of the electric eld, is affected too. Indeed, ascan be seen from Fig. 8, for the considered case, the mixed pathresults in a decreaseon the peak value of thevoltages induced onthe line midpoint. For the same case, we calculate the inducedvoltages at the line termination (Fig. 10). It can be seen fromthis gure that the effect of the ocean-land mixed propagation path on the induced voltages is different from the previous case.In fact, at the line terminations and when the lightning strikesthe land surface, as the overhead line gets closer to theocean, theinduced voltages increase, showing a relatively faster rise timewith respect to the induced voltage obtained for the homoge-neous soil characterized by the electrical properties of the land.To further evaluate this observation, we calculate the total ver-tical electric eld at ; a point 5 m right beneath the line at itstermination [see Fig. 7(b)] as shown in Fig. 11. It is clearly seenfrom this gure that the presence of the ocean-land mixed prop-agation path constructively contributes to enhancing the totalvertical electric eld at points beneath the line terminations.Hence, the induced voltage at the line termination is increasedtoo. These observations comply with the previous ndings dis-cussing the effect of soil conductivity on the lightning-inducedvoltages on overhead lines. For the considered stroke location,the presence of an ocean layer can be interpreted as if thesoil be-comes less resistive which results in an increase of the inducedvoltage at the line extremities, while the induced voltages at theline midpoint decrease [30].

B. Ocean Strike

To further evaluate the effect of the ocean-land mixed propa-gation path on the lightning-induced voltages on the ocean-sideoverhead lines, we consider another simulation case where thelightning strikes on the ocean surface. The line is matched at both sides. The lightning channel is 100 m away from theline center and equidistant to the line terminations as shown in




Fig. 12. Geometry for the calculation of lightning-induced voltages on anocean-side matched overhead line. The case of ocean strike.

Fig. 13. Induced voltages on the matched overhead line shown in Fig. 12 dueto a typical subsequent return stroke at (a) the line midpoint and (b) at theline termination . The case of ocean strike.

Fig. 12. The simulations are performed for different distances between the overhead line and the ocean. In this case, we keepthe distance between the overhead line and the lightning channelconstant. Lightning-induced voltages at the midpoint and theleft termination of the overhead line (i.e., and ) are shownin Fig. 13. As can be seen from Fig. 13(a), for the ocean strike,the induced voltages at , as the overhead line gets closer tothe ocean, slightly decrease. Note that for the considered geom-etry, the induced voltages are still less than those associated withthe homogeneous soil characterized by the properties of the landitself. Similar to the land strike, the induced voltage at the linetermination increases with the decreasing distance betweenthe line and the ocean. It is also seen from this gure that theinduced voltage is characterized by a different polarity for therst peak compared to the case in which the effect of the oceanis disregarded.

V. L IGHTNING -I NDUCED VOLTAGES ON R IVER -CROSSING

OVERHEAD L INES

To further study the effect of the mixed-propagation path, weconsider a transmission line crossing over a river referred toas the “river-crossing line” as shown in Fig. 14. The line hasa length of 1000 m, open ended at both sides, and consists

Fig. 14. Geometry for the calculation of the lightning-induced voltages on ariver-crossing overhead line. (a)Top view. (b)Side view. The caseof landstrike.

of three sections, whose middle section of length is entirelylocated above the river. The side sections are of equal length

and located above the ground at both sides of the river. We as-sume a at prole for the line at a height of 10 m above theground surface, and the river and the land are assumed to be atthe same level. We consider two different lightning strike lo-cations, namely, SL#3 (end stroke) and SL#4 (side stroke) atthe land surface for which the induced voltages on the overheadline midpoint (i.e., in Fig. 14) and both of its terminations(i.e., and in Fig. 14) are reported in Figs. 15 and 16,respectively. The lightning return stroke current is the typicalsubsequent current. A careful examination of these gures fur-ther accentuates the effect of the mixed propagation path on thelightning-induced voltages on overhead lines and the followingconclusions can be drawn:

1) For both of end and side strokes, the late time response of the induced voltages on the near termination of the river-crossing overhead line are affected by the mixed-propaga-tion path [Figs. 15(a) and 16(a)].

2) The peak value and the waveshape of the induced volt-ages at the line midpoint and the line remote terminationare markedly affected by the presence of the river. In fact,the presence of the river generally tends to increase the in-duced voltages at the line midpoint and remote termina-tion. This is more pronounced for the end-stroke case, in particular, at the line remote termination (i.e., ) whereasthe induced voltage is likely to increase by a factor of 2, showing a different polarity compared to that inducedvoltage associated with the homogeneous soil character-ized by the electrical properties of the land [Fig. 15(c)].

Similar to the ocean-side overhead line, the presented resultsfor the induced voltages should be justied by the effect of theriver on the total vertical electric-eld component. Hence, weshow in Fig. 17, this component of the electric eld at ,

, and all located 5 m beneath the line conductor [seeFig. 14(b)]. It is seen from Fig. 17 that the effect of the con-sidered mixed propagation path on the total vertical componentof the electric eld appropriately justies the same effect on theinduced voltages on the line midpoint and extremities.

It should be pointed out that in the presented simulations,the frequency dependence of soil electrical parameters has been



SHESHYEKANI AND PAKNAHAD: EFFECT OF AN OCEAN-LAND MIXED PROPAGATION PATH 235

Fig. 15. Induced voltages on the river-crossing overhead line shown inFig. 14 due to a typical subsequent return stroke striking the land at SL#3at (a) line near termination , (b) line midpoint , and (c) line remotetermination .

Fig. 16. Induced voltages on the river-crossing overhead line shown inFig. 14 due to a typical subsequent return stroke striking the land at SL#4at (a) line near termination , (b) line midpoint , and (c) line remotetermination .

disregarded. As known, this property can affect the lightning-induced voltages when the soil conductivity takes a relativelymoderate and low value 0.001 S/m) [9]–[13].

It is noted that the simulations are conducted on an Intel i7PC with 64-GB RAM. A system of linear equations is obtained

Fig. 17. Total vertical component of the electric eld at three observation points shown in Fig. 14 due to a typical subsequent return stroke striking theland at SL#3 at (a) , (b) , and (c) .

using 140167 mesh elements. For the calculation of electromag-netic elds, we used a 2-D nite-element modeling in the timedomain which takes about 30 s. However, the induced voltagesare obtained using 3-D nite-element modeling in the time do-main which takes about 15 min.

It is worth noting that the FEM has no substantial theoret-ical limitation for the calculation of lightning electromagneticelds and their associated voltages/currents on overhead linesand buried cables. However, the most limiting factor with theFEM is its prohibitive time requirement for dealing with realand long overhead lines and buried cables.

VI. C ONCLUSION

In this paper, we used a full-wave nite-element-based solu-tion of Maxwell's equations for the evaluation of the effect of an ocean-land mixed propagation path on the lightning electro-magnetic elds at different distances from the lightning channel base. It was shown that for both normal and oblique strikes, the presence of the ocean-land mixed propagation path affects theradial component of the electric eld at moderate and far dis-tances from the channel when the observation point is located intheclose vicinityof theocean. For a normal strike, theazimuthalmagnetic eld is not affected by the ocean-land mixed propaga-tion path, while for the oblique strike, this component is slightlyaffected when the observation point is very close to the ocean.The vertical electric eldis notaffected by the ocean-land mixed propagation path.

For the calculation of induced voltages, two types of overheadline were considered:

• ocean-side line where the line lays in parallel to the ocean-land interface;




• river-crossing line where the line crosses over a river.For the case of the ocean-side line, the presented simulations

have shown that for land and ocean strikes:1) the induced voltages at the line midpoint decrease with the

decreasing distance between the line and the ocean;2) the induced voltages at the line terminations increase as the

line gets closer to the ocean.For the case of the river-crossing line, the presented simula-

tions have shown that for the end and side strikes to the land:1) the late time response of the induced voltages on the near

termination of the river-crossing overhead line is affected by the mixed-propagation path;

2) the peak values and the waveshapes of the induced volt-ages at the line midpoint and the line remote terminationare markedly affected by the presence of th e river; an en-hancement as high as a factor of 2 with respect to that ob-tained by assuming a homogeneous propagation path char-acterized by the properties of the lan d might be observed.

R EFERENCES

[1] V. A. Rakov and F. Rachidi, “Overview of recent progress in light-ning research and lightning protection,” IEEE Trans. Electromagn.Compat. , vol. 51, no. 3, pp. 428–442, Aug. 2009.

[2] M. J. Master and M. A. Uman, “Transient electric and magnetic eldsassociated with establishing a nite electrostatic dipole,” Amer. J. Phys. , vol. 51, pp. 118–126, 1983.

[3] M. Rubinstein, “An approximate formula for the calculation of thehorizontal electric eld from lightning at close, intermediate, andlong range,” IEEE Trans. Electromagn. Compat. , vol. 38, no. 3, pp.531–535, Aug. 1996.

[4] F. Rachidi, “A review of eld-to-Transmission line coupling modelswith special emphasis to lightning-induced voltages,” IEEE Trans. Electromagn. Compat , vol. 54, no. 4, pp. 898–911, Aug. 2012.

[5] M. Paolone, F. Rachidi, A. Borghetti, C. A. Nucci, M. Rubinstein, V.A. Rakov, and M. A. Uman, “Lightning electromagnetic eld couplingto overhead lines: Theory, numerical simulations and experimentalvalidation,” IEEE Trans. Electromagn. Compat. , vol. 51, no. 3, pp.532–547, Aug. 2009.

[6] A. K. Agrawal, H. J. Price, and S. H. Gurbaxani, “Transient responseof multiconductor transmission lines excited by a nonuniform electro-magnetic eld,” IEEE Trans. Electromagn. Compat. , vol. EMC-22, no.2, pp. 119–129, May 1980.

[7] F. Rachidi, C. A. Nucci, M. Ianoz, and C. Mazzetti, “Inuence of lossyground on lightning induced-voltages on overhead lines,” IEEE Trans. Electromagn. Compat. , vol. 38, no. 3, pp. 404–407, Aug. 1996.

[8] C. Nucci and F. Rachidi, “Interaction of electromagnetic elds gener-ated by lightning with overhead electrical networks,” in The Lightning Flash , V. Cooray, Ed. London, U.K.: IEE, 2003, pp. 425–478.

[9] F. Delno, R. Procopio, M. Rossi, and F. Rachidi, “Inuence of fre-quency-dependent soil electrical parameters on the evaluation of light-ning electromagnetic elds in air and underground,” J. Geophys. Res. ,vol. 114, no. D11113, pp. 1–12, 2009.

[10] M. Akbari, K. Sheshyekani, and M. R. Alemi, “The effect of frequencydependence of soil electrical parameters on the lightning performanceof grounding systems,” IEEE Trans. Electromagn. Compat. , vol. 55,no. 4, pp. 739–746, Aug. 2013.

[11] R. Alipio and S. Visacro, “Frequency dependence of soil parameters:Effect on the lightning response of grounding electrodes,” IEEE Trans. Electromagn. Compat. , vol. 55, no. 1, pp. 132–139, Feb. 2013.

[12] M. Akbari, K. Sheshyekani, A. Pirayesh, F. Rachidi, M. Paolone, A.Borghetti, and C. A. Nucci, “Evaluation of lightning electromagneticelds and their induced voltages on overhead lines considering the fre-quency-dependence of soil electrical parameters,” IEEE Trans. Elec-tromagn. Compat. , vol. 55, no. 6, pp. 1210–1219, Dec. 2013.

[13] K. Sheshyekani and M. Akbari, “Evaluation of lightning-induced volt-ages on multi-conductor overhead lines located above a lossy disper-sive ground,” IEEE Trans. Power Del. , vol. 29, no. 2, pp. 683–690,Apr. 2014.

[14] G. Millington, “Ground-wave propagation over an inhomogeneoussmooth earth,” Proc. Inst. Elect. Eng.— Part III: Radio Commun. Eng. , vol. 96, pp. 53–64, 1949.

[15] K. Suda, “Field strength calculations-new method for mixed paths,”Wireless Engineer. , vol. 31, 1954.

[16] H. Bremmer, “The extension of the sommerfeld's formula for the prop-agation of radio waves over a at earth, to different conductivities of the soil,” Physica , vol. 20, pp. 441–460, 1954.

[17] J. R. Wait and L. Walters, “Curves for ground wave propagation over mixed land and sea paths,” IEEE Trans. Antennas Propag. , vol. AP-11,no. 1, pp. 38–45, Jan. 1963.

[18] J. R. Waitand L. Walters,“Correction to curves for ground wave propa-gation over mixed land and sea paths,” IEEE Trans. Antennas Propag. ,vol. AP-11, no. 3, p. 329, May 1963.

[19] A.Shoory, A.Mimouni, F.Rachidi,V. Cooray,and M.R ubinstein, “Onthe accuracy of approximate techniques for the evaluation of lightningelectromagnetic elds along a mixed propagation path,” Radio Sci. ,vol. 46, no. RS2001, 2011.

[20] Q. Zhang, D. Li, X. Tang, and Z. Wang, “Lightning-radiated horizontalelectric eld over a rough- and ocean-land mixed propagation path,” IEEE Trans. Electromagn. Compat. , vol. 55, no. 4, pp. 733–737, Aug.2013.

[21] Q. Zhang, D. Li, Y. Fan, Y. Zhang, and J. Gao, “Examination of the Cooray-Rubinstein (C-R) f ormula for a mixed propagation path by using FDTD,” J. Geophys. Res. , vol. 117, no. D15309, pp. 1–7,2012.

[22] Q. Zhang, X. Tang, J. Gao, L. Zhang, and D. Li, “The inuence of thehorizontally stratied conducting ground on the lightning-induced volt-

ages,” IEEE Trans. Electromagn. Compat. , vol. 56, no. 2, pp. 435–443,Apr. 2014.[23] J. Paknahad, K. Sheshyekani, and F. Rachidi, “Lightning electromag-

netic elds and their induced currents on buried cables. Part I: the Ef-fect of an Ocean-Land Mixed Propagation Path,” IEEE Trans. Electro-magn. Compat. , 2014, to be published.

[24] J. Paknahad, K. Sheshyekani, F. Rachidi, and M. Paolone, “Lightningelectro magnetic elds and their induced currents on buried cables. PartII: the Effect of a Horizontally Stratied Ground,” IEEE Trans. Elec-tromagn. Compat. , 2014, to be published.

[25] COMSOL multiphysics software package, 2011. [Online]. Available:http://www.comsol.com

[26] “COMSOL RF Module User's Guide,” COMSOL, Inc., Stockholm,Sweden, 2011.

[27] F. Rachidi, W. j. Janischewsky, A. M. Hussein, C. A. Nucci, S. Guer-rieri, B. Kordi, and J. S. C. hang, “Current and electromagnetic eldassociated with lightning return strokes to tall towers,” IEEE Trans.

Electromagn. Compat. , vol. 43, no. 3, pp. 356–367, Aug. 2001.[28] F. Heidler, “Analytische blitzstrom funktion zur LEMP-berechnung,”

in Proc. 18th Int. Conf. Lightning Protect. , Munich, Germany, Sep.1985, pp. 63–66.

[29] F. Rachidi, C. A. Nucci, M. Ianoz, and C. Mazzetti, “Inuence of lossyground on lightning induced-voltages on overhead lines,” IEEE Trans. Electromagn.Compat. , vol. 38, no. 3, pp. 404–407, Aug. 1996.

[30] C. A. Nucci and F. Rachidi, “Interaction of electromagnetic elds gen-erated by lightning with overhead electrical networks,” in The Light-ning Flash , V. Cooray, Ed. London, U.K.: Inst. Eng. Technol, 2003,ch. 8.

Keyhan Sheshyekani (M'10–SM'13) received the B.S. degree in electricalengineering from Tehran University, Tehran, Iran, in 2001, and the M.S. and

Ph.D. degrees in electrical engineering from Amirkabir University of Tech-nology (Tehran Polytechnique), Tehran, Iran, in 2003 and 2008, respectively.

He was with Ecole Polytechnique, Federale de Lausanne (EPFL), Lausanne,Switzerland, in 2007 as a Visiting Scientist and later as a Research Assistant.He was an Invited Professor at the EPFL in 2014. Currently, he is an AssistantProfessor of Electrical Engineering with Shahid Beheshti University, Tehran.His research interests include power system modeling and simulation, smartgrid, microgrids, and electromagnetic compatibility.

Javad Paknahad (S'14) was born in Iran in 1989. He received the B.S. degreein electrical engineering from Tafresh campus, Amirkabir University of Tech-nology (Tehran Polytechnique), Tehran, Iran, in 2011 and the M.S. degree inelectrical engineering from Shahid Beheshti University, Tehran, in 2013.

Currently, he is a Research Assistant at the Power System Laboratory, Shahid

Beheshti University. His research interests include power system modeling andsimulations, electromagnetic compatibility, and the application of electromag-netics in power systems.

Documents

The Effect of an Ocean-Land Mixed Propagation Path on the Lightning Electromagnetic Fields and Their Induced Voltages on Overhead Lines